Final answer:
The volume of the pressure vessel can be calculated using the ideal gas law PV = nRT by rearranging to V = nRT/P and ensuring all units are consistent. Temperature must be in Kelvin, and the pressure must match the units of the gas constant R for the equation to work correctly.
Step-by-step explanation:
To determine the volume of the pressure vessel, we use the ideal gas equation, PV = nRT, where:
P is the corrected pressure in atmospheres (atm) or Pascals (Pa), depending on the value of the gas constant R used.
V is the volume in liters (L) or cubic meters (m3), again depending on the units of R.
n is the number of moles of the gas.
T is the temperature in Kelvin (K), which can be converted from Celsius by adding 273.15 to the Celsius temperature.
R is the universal or ideal gas constant whose value depends on the units being used for pressure and volume in the equation.
To solve for volume V, we need to rearrange the ideal gas equation to V = nRT/P. Before applying this formula, ensure that the pressure P is in the correct units to match the constant R, and that temperature T is converted to Kelvin. If using the R value of 0.08206 L atm mol-1 K-1, ensure P is in atmospheres and V will be in liters. If using R as 8.314 kPa L mol-1 K-1, then P should be in kilopascals and V in liters, or for 8.3145 J/(K•mol), P should be in Pascals (Pa) and V in cubic meters (m3).